Michael, Try holding the jump ring in stainless steel tweezers
held in a vise. The points on your third hand are acting as heat
sinks taking heat away from the joint. Stainless seems not to
conduct as well. I do this sort of thing quite often using a #4
tip on a “Little Torch” with a high flame just below the point
where you would melt the ring. Suggest suspending the whole thing
except, the ring of course ,in a small container of water, place
the flux and solder chip on the joint and blast it. Might take a
little practice, but it works for me.
Jerry in Kodiak where the bears are finally coming out of their
winter dens.